I wouldn't ditch the carb body or the slide, they aren't going to be cheap to replace, and you'll probably end up having to go the ebay route and buying a whole rack to use for parts.
You can drill out the head of the stripped screw holding the backing plate in place that holds the slide needle. You just need the right sized bit and a steady hand. In fact, I would wrap the slide in some cloth and carefully snug it up in a vice, and maybe use a rubber-band or something to hold the slide linkage arm to one side giving you a clear shot at the screw head. Once you get it out, I'd consider replacing all those tiny screws with allen heads...
As for the jet you broke off, I'm going to defer to someone with more experience, but I am sure there is a way to extract the threads. I would say just go to the hardware and get an extractor bit, but it's going to take a very small one and I'm not sure you'll find one in a normal hardware...
For slow jets, I would order from Service Honda (
http://www.servicehondapsn.com/fiche_select.asp), or just have your local honda dealer order you some (they'll charge you $9 each, though).